The two main continuations now are 6.Qh5+ and 6.d4. Which move you chose is mostly a question of the kind of game you like.
6.Qh5+ g6 also allows White to capture a piece, and can lead to two complex defenses, after 7.Qxe5 Qe7 or 7...d6. The better prepared player is more likely to win. Unprepared defenders are likely to drop at least a Rook, however.
6.Qh5+ Ke6 is the sign of a player who is familiar with the Jerome Gambit, and who has prepared a particular defense - or it is the sign of a player who is unfamiliar with the Jerome and who hopes against hope that he can hang on to all of the captured material and survive.
6.d4 Bxd4 Qxd4 is less forcing than the 6.Qh5+ lines, and this can actually be difficult for Black - having to figure things out on his own. In the meantime, White develops, decides which pawns to advance, and even which side to castle on.
Other ways for Black to deal with 6.d4 run into the same problem, that of the defender having to put a whole defense together without much help from White.
Which lines do I like or loathe? I prefer 6.Qh5+, because I am uneasy with the positions after 6.d4 Qh4!? - the one time I tried the line, perrypawnpusher - 4xel, Chess.com, 2017 (1/2-1/2, 29), I had to weasel my way out of a difficult situation. Bill Wall, on the other hand, plays 6.d4 regularly, and rarely sees 6...Qh4, anyhow. I am not afraid of 6.Qh5+ g6, but I always follow my rule: Do not take the Rook at h8. I am happy to see 6.Qh5+ Ke6, but after the possible move 7.f4, often the answer 7...d6 creates difficulties.
A balanced diet of playing and studying the Jerome Gambit should provide plenty of enjoyment in your chessic activitied.